Optimal Experimental Designs for Estimating Henry's Law Constants via the Method of Phase Ratio Variation

When measuring Henry's Law constants ($k_H$) using the phase ratio method via headspace gas chromatography (GC), the value of $k_H$ of the compound under investigation is calculated from the ratio of the slope to the intercept of a linear regression of the the inverse GC response versus the ratio of gas to liquid volumes of a series of vials drawn from the same parent solution. Thus, an experimenter will collect measurements consisting of the independent variable (the gas/liquid volume ratio) and dependent variable (the inverse GC peak area). There is a choice of values of the independent variable during measurement. A review of the literature found that the common approach is a simple uniformly spacing of the liquid volumes. We present an optimal experimental design which estimates $k_H$ with minimum error and provides multiple means for building confidence intervals for such estimates. We illustrate efficiency improvements of our new design with an example measuring the $k_H$ for napthalene in aqueous solution as well as simulations on previous studies. The designs can be easily computed using our open source software optDesignSlopeInt, an R package on CRAN. We also discuss applicability of this method to other fields.